Class 11 Maths Statistics Notes

Statistics – Class 11 Maths (NCERT Based)

The chapter Statistics introduces students to collecting, organizing, and analyzing data. It is widely used in probability, economics, research, and data interpretation.

This content strictly follows the NCERT Class 11 Maths syllabus and explains concepts in a student-friendly and exam-oriented manner.

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📖 1. Introduction

Statistics deals with:

1. Collection of data
2. Organization of data
3. Presentation of data
4. Analysis and interpretation of data

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🔹 2. Types of Data

1. Raw Data: Unprocessed information
   • Example: Marks of students: 45, 50, 55, 60
2. Grouped Data: Data arranged in classes or intervals
   • Example: Marks (0–10, 10–20, …)

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🔹 3. Measures of Central Tendency

Central tendency indicates the central value of a data set.

3.1 Mean (Arithmetic Mean)

• Definition: Average of all observations
• Formula:
  • For ungrouped data: $\bar{x} = \frac{\sum x_i}{n}$xˉ=n∑xi​​
  • For grouped data: $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$xˉ=∑fi​∑fi​xi​​

3.2 Median

• Definition: Middle value of ordered data
• For grouped data:

$$\text{Median} = l + \frac{\frac{N}{2} – CF}{f} \cdot h$$Median=l+f2N​−CF​⋅h

Where:

• l = lower boundary of median class
• N = total frequency
• CF = cumulative frequency before median class
• f = frequency of median class
• h = class width

3.3 Mode

• Definition: Value that occurs most frequently
• For grouped data:

$$\text{Mode} = l + \frac{f_1 – f_0}{2f_1 – f_0 – f_2} \cdot h$$Mode=l+2f1​−f0​−f2​f1​−f0​​⋅h

Where:

• l = lower boundary of modal class
• f₁ = frequency of modal class
• f₀ = frequency of previous class
• f₂ = frequency of next class
• h = class width

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🔹 4. Measures of Dispersion

Dispersion indicates how spread out the data is.

1. Range: Difference between largest and smallest values $$R = x_{max} – x_{min}$$R=xmax​−xmin​
2. Mean Deviation (MD): Average absolute deviation from mean $$MD = \frac{\sum |x_i – \bar{x}|}{n}$$MD=n∑∣xi​−xˉ∣​
3. Variance (σ²): Average of squared deviations from mean $$\sigma^2 = \frac{\sum (x_i – \bar{x})^2}{n}$$σ2=n∑(xi​−xˉ)2​
4. Standard Deviation (σ): Square root of variance $$\sigma = \sqrt{\sigma^2}$$σ=σ2​